Berry D A, Herzel H, Titze I R, Krischer K
Department of Speech Pathology and Audiology, University of Iowa, Iowa City 52242.
J Acoust Soc Am. 1994 Jun;95(6):3595-604. doi: 10.1121/1.409875.
Empirical orthogonal eigenfunctions are extracted from biomechanical simulations of normal and chaotic vocal fold oscillations. For normal phonation, two dominant empirical eigenfunctions capture the vibration patterns of the folds and exhibit a 1:1 entrainment. The eigenfunctions show some correspondence to theoretical low-order normal modes of a simplified, three-dimensional elastic continuum, and to the normal modes of a linearized two-mass model. The eigenfunctions also facilitate a physical interpretation of energy transfer mechanisms in vocal fold dynamics. Subharmonic regimes and chaotic oscillations are observed during simulations of a lax cover, in which case at least three empirical eigenfunctions are necessary to capture the resulting vocal fold oscillations. These chaotic oscillations might be understood in terms of a desynchronization of a few of the low-order modes, and may be related to mechanisms of creaky voice or vocal fry. Furthermore, some of the empirical eigenfunctions captured during complex oscillations correspond to higher-order normal modes described in earlier theoretical work. The empirical eigenfunctions may also be useful in the design of lower-order models (valid over the range for which the empirical eigenfunctions remain more or less constant), and may help facilitate bifurcation analyses of the biomechanical simulation.
经验正交特征函数是从正常和混沌声带振荡的生物力学模拟中提取的。对于正常发声，两个主要的经验特征函数捕捉了声带的振动模式，并呈现出1:1的同步。这些特征函数与简化的三维弹性连续体的理论低阶正常模式以及线性化双质量模型的正常模式有一定的对应关系。这些特征函数还便于对声带动力学中的能量传递机制进行物理解释。在模拟松弛覆盖层时观察到次谐波状态和混沌振荡，在这种情况下，至少需要三个经验特征函数来捕捉由此产生的声带振荡。这些混沌振荡可以从少数低阶模式的失步角度来理解，并且可能与嘎吱声或发声破裂机制有关。此外，在复杂振荡过程中捕获的一些经验特征函数与早期理论工作中描述的高阶正常模式相对应。经验特征函数在低阶模型的设计中也可能有用（在经验特征函数或多或少保持恒定的范围内有效），并且可能有助于促进生物力学模拟的分岔分析。
